What is some characterizing description of what such graphs look like?

By edge-maximal I mean that adding any edge (without increasing the number of vertices) makes the graph 3-vertex-connected.

  • $\begingroup$ $$\overline{K_{m,n}+2K_1}?$$ $\endgroup$ – bof Jul 13 '16 at 18:17
  • $\begingroup$ What does the bar mean? $\endgroup$ – Damian Reding Jul 13 '16 at 18:21
  • $\begingroup$ Graph complement. $\endgroup$ – bof Jul 13 '16 at 18:29
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    $\begingroup$ Likewise I guess $\overline{K_{m,n}+pK_1}$ is a general expression for an edge-maximal graph of connectivity $p.$ However, I am seriously sleep-deprived, so don't take my word for anything. $\endgroup$ – bof Jul 13 '16 at 18:36

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